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Title:Dynamics of a fully stochastic discretized neuronal model with excitatory and inhibitory neurons
Author(s):Berning, Stephen R
Director of Research:DeVille, Lee
Doctoral Committee Chair(s):Rapti, Zoi
Doctoral Committee Member(s):Kirkpatrick, Kay L; Zharnitsky, Vadim
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):neural network
neuronal network
inhibitory neurons
mean-field analysis
limit theorem
Abstract:We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons where synapses are failure-prone. It was shown that this model exhibits different metastable phases of asynchronous and synchronous behavior, since the model limits on a mean-field deterministic system with multiple attractors. Our work investigates adding inhibition into the model. The new model exhibits the same metastable phases, but also exhibits new non-monotonic behavior that was not seen in the DeVille et al. model. The techniques used by DeVille et al. for finding the mean-field limit are not suitable for this new model. We explore early attempts at obtaining a new mean-field deterministic system that would give us an understanding of the behavior seen in the new model. After redefining the process we do find a mean-field deterministic system that the model limits on, and we investigate the behavior of the new model studying the mean-field system.
Issue Date:2015-07-16
Rights Information:Copyright 2015 Stephen Berning
Date Available in IDEALS:2015-09-29
Date Deposited:August 201

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